$-3tu + 10tv + 2t - 4 = -10u - 10$ Solve for $t$.
Solution: Combine constant terms on the right. $-3tu + 10tv + 2t - {4} = -10u - {10}$ $-3tu + 10tv + 2t = -10u - {6}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $-3{t}u + 10{t}v + 2{t} = -10u - 6$ Factor out the $t$ ${t} \cdot \left( -3u + 10v + 2 \right) = -10u - 6$ Isolate the $t$ $t \cdot \left( -{3u + 10v + 2} \right) = -10u - 6$ $t = \dfrac{ -10u - 6 }{ -{3u + 10v + 2} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{10u + 6}{3u - 10v - 2}$